In medical devices for extracorporeal blood treatment (dialysis) tube roller pumps are frequently used, which convey the blood drawn from the patient to a dialyzer and return it to the patient. Such tube roller pumps operate peristaltically, with a loop-shaped tube segment abutting on an appropriately curved running surface of the pump housing. A pump rotor, which is located within the running surface, then moves with its outer edges, or rather with rollers attached thereto, along the tube segment. In so doing, it locally squeezes the tube thus allowing, on the basis of the elastic properties of the material of the tube segment, blood to be conveyed through the tube segment. To this end, the blood is supplied to the tube segment via a first connection and removed therefrom via a further connection at the other end of the tube segment. The tube segment thus forms, e.g. together with the supply and discharge lines and a plurality of air traps, a so-called transfer system with which the patient's blood is conveyed to a dialyzer and back to the patient.